A Family of Curl-Curl Conforming Finite Elements on Tetrahedral Meshes (CSIAM Transactions on Applied Mathematics, 2020)
In [23], we, together with our collaborator, proposed a family of $H$(curl$^2$)-conforming elements on both triangular and rectangular meshes. The elements provide a brand new method to solve the quad-curl problem in 2 dimensions. In thispaper, we turn our focus to 3 dimensions and construct $H$(curl$^2$)-conforming finiteelements on tetrahedral meshes. The newly proposed elements have been proved tohave the optimal interpolation error estimate. Having the tetrahedral elements, we cansolve the quad-curl problem in any Lipschitz domain by the conforming finite elementmethod. We also provide several numerical examples of using our elements to solvethe quad-curl problem. The results of the numerical experiments show the correctnessof our elements.